What are the odds?

Question

What are the odds of rolling 6 of a kind from 6 dice? I just did it and wanted to know the stats

Answer 1

There is a one in 46656 (6^6) chance of rolling all sixes with six dice (all of which are six-sided). There is a one in 7776 (6^6 / 6) chance of rolling all six as one number (such as 1-1-1-1-1-1 or 2-2-2-2-2-2).

Answer 2

First, notice that there is a difference between 6 of any kind and 6 of a particular kind.

For any kind, notice that it doesn't matter what you roll on the first roll, it only matters that the next 5 rolls match it.

p(any # on roll 1) = 1

now every subsequent roll must match,
there's a p=1/6 prob of getting that number
yielding

p( rolling the same number 6 times ) = (1/6)^5 = 1/1776

Notice that if you had asked for rolling a particular number 6 times it would be (1/6)^6

The post above mine makes a distinction between rolling the dice simultaneously and rolling them together. Why would it make a difference? The dice have no memory and no way of knowing what the others are doing!

Answer 3

The first die could be any value.... since you didn't say six-sixes or something so it could be 2 or four or whatever....

The next dice has to match so 1 chance in six. Then the NEXT dice has to match, another 1 in six, and you do that five times,

So

1 in (6 * 6 * 6 * 6 * 6) or 1 in 6^5

1 in 7776

Answer 4

T
Lets start with the odds of getting (lets say 3) from one dice.
the odds would be 1/6. The odds for getting 2 3's would be 1/6 for the first dice and 1/6 for the second one. That would give us a probability of 1/36. For six dice would be 1/6*1/6*1/6*1/6*1/6*1/6.
1 in 46656.
You are lucky.
This is in case you rolled them altogether at the same time, not one by one.

Answer 5

1/6*6*6*6*6 or 1 in 7776!

Answer 6

1 in 46,656
Perhaps you should visit Las Vegas.

Answer 7

i believe its like one in six